Not really a difference. It's essentially an idiomatic suggestion, nowadays. "Let us" would literally translate as "allow us", but it more closely means "we should/should we/how about we/why don't we".

Saying "let us" only differs from "let's" in nuance. They mean exactly the same thing. "Let us" might be a bit more formal because it's not a contraction. Or it might be used emphatically. "Let's" is fast, it's easy to say, more suited for fast speech or making a 'quick suggestion'. Also, it can take away emphasis from the "us" and so cause the emphasis to be placed on the verb: "Let's GO".

They're completely interchangeable, though. Say whichever your prefer, no one should 'bat an eye-lash'. Rather, it's unlikely anyone will care, even if they notice.

Let us go to the restaurant=Please allow us to go to the restaurant. Yes, 'let us' is frequently used as a request for permission, but to make it a polite request, the word 'please' (for example) would usually precede 'let us'. When used to request permission, 'us' would not normally include the person whose permission is being requested.

Let's go to the restaurant=Shall we go to the restaurant. Yes, this would always be understood as a suggestion, and the contracted word 'us' would include the person or people you're speaking to.

I guess you are right let`s ) includes both the speaker and the hearer . It`s inclusive . It expresses suggestion. Notice the tag question : let`s play tennis, shall we ? but ( let us ) is confined to the speaker only : it`s exclusive . It expresses permission . Notice the tag question :let us go to the cinema, will you ?Am I correct ?????

AnonymousI guess you are right let`s ) includes both the speaker and the hearer . It`s inclusive . It expresses suggestion. Notice the tag question : let`s play tennis, shall we ? but ( let us ) is confined to the speaker only : it`s exclusive . It expresses permission . Notice the tag question :let us go to the cinema, will you ?Am I correct ?

Both readings of 'Let us' are possible (see the verified posts above).

T.S. Eliot wrote this:

LET us go then, You and I, When the evening is spread out against the sky Like a patient etherized upon a table; Let us go, through certain half-deserted streets, The muttering retreatsOf restless nights in one-night cheap hotels And sawdust restaurants with oyster-shells: Streets that follow like a tedious argument Of insidious intent To lead you to an overwhelming question ...Oh, do not ask, "What is it?" Let us go and make our visit.